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Integral of Composition Functions

  1. Oct 23, 2012 #1
    1. The problem statement, all variables and given/known data

    http://sphotos-h.ak.fbcdn.net/hphotos-ak-snc6/282312_368248176595083_1229435302_n.jpg [Broken]

    2. Relevant equations

    To subtitute x into U, but that did not work.

    3. The attempt at a solution

    I have tried subtituting x into U like this :

    http://sphotos-g.ak.fbcdn.net/hphotos-ak-snc7/578486_368249266594974_1874868606_n.jpg [Broken]

    The last two lines are my "goofing around" answer. :tongue2:
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Oct 23, 2012 #2
    If you change variables, you have to change them all! You can't just leave some x's laying around. Now you have x=x(u) and you don't know how this integrates.

    There is kind of a standard trick for any integral that looks like this, which is to first complete the square. What you want to do is to write the integrand into a form
    [tex] \frac{dx}{\sqrt{A^2 - (B+Cx)^2}} [/tex]
    and then do a trigonometric substitution [itex]B+Cx = A \sin t [/itex]
     
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